Lobbying is trying to persuade decision makers to see a certain issue your way. Bribery is paying decision makers to do what you want.
The difference is in the "persuading" part: a lobbyist wants to convince the decision maker to agree with them. Whereas when you bribe someone, you fully expect them to disagree with you, but still do what you want because you pay them.
Or looking at it from the other direction: a decision maker that has been persuaded by a lobbyist believes that the choice they are making is the right choice. A decision maker that has been bribed, knows that the choice they are making is the wrong one, but they make it anyway because they are paid to.
An important differentiator is that a bribe is an exchange: "I give you money, in exchange, you vote 'Yes'". Whereas lobbying is more like: "Here is a list of all the reasons why I think voting 'Yes' is the right thing to do".
Note: this obviously does not mean that there aren't people who pretend to be lobbying but are actually bribing, nor does it mean there aren't decision makers who claim to be lobbied, when they are actually being bribed.
It's also sometimes not easy to draw a precise line between the two. Let's say, I happen to think that solar power is good both for the environment and the economy, and I invite a group of politicians to my downtown office for a workshop where I explain to them exactly the environmental and economic benefits of solar power. Considering that my workshop takes several hours, I of course provide food and beverages. And since I invited them to come to a place they would normally not have gone to, I offer to cover their transportation cost. Lastly, since I am taking up basically an entire day of their time, I am paying them a stipend equivalent to about one day's pay for an average middle-class white collar salaried employee.
Is that bribery? I mean, I did pay them money! I would argue that it is still lobbyism, since they would probably have been better off not coming to my workshop.
Now, let's say my workshop does not take one day but an entire week (but with only one 4 hour session each day and the rest of the day is free), and it does not take place in my downtown office, but in Hawaii, and I not only invite the politicians but also their families, and I cover their flights, hotels, etc.
Is that lobbyism? After all, it is not structurally different from the example before!
What if I am inviting the politicians to some exotic tropical place for two days, but that exotic tropical place happens to be fully solar-powered by one of the world's most advanced solar farms, and there happens to be no similar place closer to home than this one?